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Popular >

f(t)=6e^{5t}+e^{-3t}-9

Solution

f (t) = 6 e^{5 t} + e^{- 3 t} - 9

Solution

Domain : - \infty < t < \infty

Range : f (t) \geq \frac{6}{e ^{\frac{5 l n ( 10 )}{8}}} + e^{\frac{3 l n ( 10 )}{8}} - 9

X Intercepts : (ln (0.48360 \dots), 0), (ln (1.06366 \dots), 0), Y Intercepts : (0, - 2)

Asymptotes : None

Extreme Points : Minimum (- \frac{ln ( 10 )}{8}, \frac{6}{e ^{\frac{5 l n ( 10 )}{8}}} + e^{\frac{3 l n ( 10 )}{8}} - 9)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{6}{e ^{\frac{5 l n ( 10 )}{8}}} + e^{\frac{3 l n ( 10 )}{8}} - 9, \infty)

Solution steps

Domain of

6 e^{5 t} + e^{- 3 t} - 9 : - \infty < t < \infty

Range of

6 e^{5 t} + e^{- 3 t} - 9 : f (t) \geq \frac{6}{e ^{\frac{5 l n ( 10 )}{8}}} + e^{\frac{3 l n ( 10 )}{8}} - 9

Axis interception points of

6 e^{5 t} + e^{- 3 t} - 9 :

X Intercepts

: (ln (0.48360 \dots), 0), (ln (1.06366 \dots), 0),

Y Intercepts

: (0, - 2)

Asymptotes of

6 e^{5 t} + e^{- 3 t} - 9 :

None

Extreme Points of

6 e^{5 t} + e^{- 3 t} - 9 :

Minimum

(- \frac{ln ( 10 )}{8}, \frac{6}{e ^{\frac{5 l n ( 10 )}{8}}} + e^{\frac{3 l n ( 10 )}{8}} - 9)

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Frequently Asked Questions (FAQ)

What is the f(t)=6e^{5t}+e^{-3t}-9 ?
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